Termination of cardiac Ca²⁺ sparks: An investigative mathematical model of calcium-induced calcium release

A Ca²⁺ spark arises when a cluster of sarcoplasmic reticulum (SR) channels (ryanodine receptors or RyRs) opens to release calcium in a locally regenerative manner. Normally triggered by Ca²⁺ influx across the sarcolemmal or transverse tubule membrane neighboring the cluster, the Ca²⁺ spark has been shown to be the elementary Ca²⁺ signaling event of excitation-contraction coupling in heart muscle. However, the question of how the Ca²⁺ spark terminates remains a central, unresolved issue. Here we present a new model, "sticky cluster," of SR Ca²⁺ release that simulates Ca²⁺ spark behavior and enables robust Ca²⁺ spark termination. Two newly documented features of RyR behavior have been incorporated in this otherwise simple model: "coupled gating" and an opening rate that depends on SR lumenal [Ca²⁺]. Using a Monte Carlo method, local Ca²⁺-induced Ca²⁺ release from clusters containing between 10 and 100 RyRs is modeled. After release is triggered, Ca²⁺ flux from RyRs diffuses into the cytosol and binds to intracellular buffers and the fluorescent Ca²⁺ indicator fluo-3 to produce the model Ca²⁺ spark. Ca²⁺ sparks generated by the sticky cluster model resemble those observed experimentally, and Ca²⁺ spark duration and amplitude are largely insensitive to the number of RyRs in a cluster. As expected from heart cell investigation, the spontaneous Ca²⁺ spark rate in the model increases with elevated cytosolic or SR lumenal [Ca²⁺]. Furthermore, reduction of RyR coupling leads to prolonged model Ca²⁺ sparks just as treatment with FK506 lengthens Ca²⁺ sparks in heart cells. This new model of Ca²⁺ spark behavior provides a "proof of principle" test of a new hypothesis for Ca²⁺ spark termination and reproduces critical features of Ca²⁺ sparks observed experimentally.